An on-going debate surrounds the relationship between specific language impairment and developmental dyslexia, in particular with respect to their phonological abilities. Are these distinct disorders? To what extent do they overlap? Which cognitive and linguistic profiles correspond to specific language impairment, dyslexia and comorbid cases? At least three different models have been proposed: the severity model, the additional deficit model and the component model. We address this issue by comparing children with specific language impairment only, those with dyslexia-only, those with specific language impairment and dyslexia and those with no impairment, using a broad test battery of language skills. We find that specific language impairment and dyslexia do not always co-occur, and that some children with specific language impairment do not have a phonological deficit. Using factor analysis, we find that language abilities across the four groups of children have at least three independent sources of variance: one for non-phonological language skills and two for distinct sets of phonological abilities (which we term phonological skills versus phonological representations). Furthermore, children with specific language impairment and dyslexia show partly distinct profiles of phonological deficit along these two dimensions. We conclude that a multiple-component model of language abilities best explains the relationship between specific language impairment and dyslexia and the different profiles of impairment that are observed.